1. INTRODUCTION

In 1964,
Penzias & Wilson
(1965)
serendipitously detected the
microwave background as anomalous excess noise, coming from all
directions and corresponding to a temperature of ~ 3 K. This was
immediately interpreted as being a relic of the Primeval Fireball by
Dicke et al (1965),
who had already been preparing an experiment in
the hope of detecting it. Recently the remarkable success of the FIRAS
instrument on the COBE satellite has confirmed that the cosmic
microwave background radiation has a Planck spectrum with
(Mather et al. 1994)

(1)

The blackbody nature of the cosmic microwave background (CMB)
strongly suggests an origin in the early universe. In the standard Big
Bang model thermalization occurred at an epoch
t 1 yr or
T
107 K. By 1975, the remote origin of the CMB was supported by
the high
degree of isotropy apart from the detection of the dipole anisotropy
(Corey & Wilkinson
1976,
Smoot et al 1977).
The best-fitting dipole is
Dobs = 3.343 ± 0.016 mK (95% CL) towards
(, b) = (264.°4
± 0.3, 48.°4 ± 0.°5)
(Smoot et al 1991,
1992;
Kogut et al 1993;
Fixsen et al 1994).
After correction for the motion of the Earth around the Sun,
the Sun around the Galaxy, and the Galaxy relative to the center of
mass of the Local Group, one infers
(Smoot et al 1991,
Kogut et al 1993)
that our Local Group of galaxies is moving at a velocity of
627 ± 22 km s-1 in a direction
(, b) = (276°
± 3°, 30° ± 3°). Convergence
of the local velocity vectors to the CMB dipole does not occur until a
distance of > 100h-1 Mpc (herein the Hubble constant
H0 = 100h km s-1
Mpc-1), according to the dipole measured in the IRAS all-sky
galaxy redshift survey
(Strauss et at 1992),
and possibly to > 150h-1 Mpc if
the recent claim of a dipole in the nearby Abell cluster frame is
confirmed
(Lauer & Postman 1992,
1993;
see also
Plionis & Valdarnini
1991).
Theoretical arguments actually suggest that convergence may
only be logarithmic
(Juszkiewicz et al 1990)
if the large-scale
density fluctuation spectrum has the Harrison-Zel'dovich form,
/
-(n+3)/2
with n = 1
(Harrison 1970,
Peebles & Yu 1970,
Zel'dovich 1972).

After 1980, the inflationary cosmology (see
Narlikar & Padmanabhan
1991
for a review) revived interest in non-baryonic dark matter, now
considered more likely to be of the cold variety (e.g.
Peebles 1982a,
Blumenthal et at 1984,
Frenk et al 1990).
The hot/cold classification
(Bond & Szalay 1983)
amounts to the velocity dispersion of the
candidate particle being much greater or much less than the canonical
escape velocity of a typical galaxy: ~ 300 km s-1 at the epoch
of equal densities of matter and radiation, 1 + zeq =
23,900(0h2). Only at
later times does substantial sub-horizon fluctuation growth occur.

As limits improved on small-scale fluctuations, to
T / T ~
10-4
(Uson & Wilkinson
1984a,
b,
c),
refined theoretical estimates showed that,
with the aid of dark matter, one could further reduce
T / T
by an order of magnitude. (For a summary of the pre-COBE experimental
situation see
Partridge 1988,
Readhead & Lawrence
1992).
The experimental breakthrough came in 1992
(Smoot et al 1992)
with the first detection
of large angular scale anisotropies of cosmological origin in the CMB
by the COBE DMR experiment
(Smoot et al 1990).
This has since been confirmed by at least one other experiment
(Ganga et al 1993).
Because of the sky coverage and frequency range spanned, one can now, with
confidence, eliminate any Galactic explanation, as well as the
possibility that nearby superclusters containing diffuse hot gas are
imprinting Sunyaev-Zel'dovich fluctuations on the CMB
(Hogan 1992;
Rephaeli 1993a,
b;
Bennett et al 1993).
This conclusion is further
strengthened by the lack of correlation with the X-ray background
(Boughn & Jahoda 1993).
Fluctuations are telling us about density perturbations at
z ~ 1000. The first year DMR data represent a >
7
detection; the best determined measurement is the sky variance on
scales of 10°,
obs(10°)
= 30 ± 5µK
(Smoot et al 1992).

Several other experiments have subsequently reported detections on
intermediate angular scales, ~ 1° (with nine separate claims of
detection of fluctuations by the end of 1993). These are all generally
consistent with the COBE amplitude, given plausible extrapolation
from the large angular scales, as described below, although there is cause
for serious concern about foreground Galactic contamination as a
consequence of limited sky and frequency coverage.

We are certainly now on the verge of a quantum leap in cosmological
modeling. Large-scale "seed" power has been discovered at a level of
T / T ~
10-5. These fluctuations are the fossil precursors
of the largest structures we see today, which have scales of
50h-1
Mpc. On angular scales
10°, they are also
relics of the apparently noncausal
initial conditions in the Big Bang, which can be accounted for by
inflationary cosmology, and hence provide a possible verification of
inflation. Gravity waves are another legacy from inflation, and can
leave a distinguishable signature imprinted on the CMB [see
Burke (1975) and
Doroshkevich et al (1977)
for a pre-inflation
view]. Indeed, there have been recent proposals to utilize the CMB
fluctuations on large scales to reconstruct the inflaton potential.

The connection between large-scale power in the matter distribution
and that in the CMB is conceptually simple, if at early epochs one is
in the linear regime. At large redshift, a comoving scale of 100 Mpc
projects to an angular scale of approximately
0h
degrees. Complications arise for several reasons. First, the statistical
properties of the fluctuations are not known a priori. Inflation
predicts that the fluctuations are Gaussian. However, in
non-inflationary cosmologies, especially likely if
0 < 1 as
favored by observations of the local universe, the initial conditions are
non-Gaussian. Moreover, one may have non-linear topological defects as
the source of seed density fluctuations. We cannot yet predict with
much confidence the likely implications of such models for CMB
anisotropies, largely because the connection with large-scale
structure observations, to which the theory must ultimately be
normalized, is tenuous.

Given an initial spectrum of density fluctuations,
(k), one can
calculate the transfer function to obtain the radiation power spectrum
Prad(k). The scale
zeq
(h2) is imprinted, thereby inevitably
guaranteeing a dependence proportional both to
0 and, when
normalized to an observed scale, to H0. Curvature can
complicate the matter further since, in a low
0
universe, on scales larger than the curvature radius there is no unique
definition of the matter fluctuation power spectrum.

Other cosmological model parameters that enter less directly are
B,
and
, the contributions to
0 in
baryons, vacuum, and massive
neutrinos, respectively. These all modify the detailed transfer
function for a given
(k). The
ionization history of the Universe is
yet another unknown. The intergalactic medium is highly ionized at
z = 5. If it were even 90% ionized at
z 20, the
modification of the predicted
T / T
can become significant, at the 10-20% level, on angular
scales of a few degrees. If ionization occurred much earlier, there is
strong smoothing of degree-scale fluctuations, but at the cost of
regenerating them, together with subarcminute-scale fluctuations in
second order, on the new last scattering surface.

This review is arranged as follows.
Section 1 presents an overview of
recombination, and introduces the various sources of temperature
fluctuations. Section 2 summarizes structure
formation theory, and the
different fluctuation modes. The power spectrum formalism is described
in Section 3. In
Section 4, we review Gaussian autocorrelation
function
fitting, window functions, and alternative approaches to data analysis.
Higher order effects (such as reionization) are described in
Section 5.
Problems arising from various types of uncertainties are summarized in
Section 6.
Section 7 discusses alternatives to the
"standard" model and
Section 8 describes some issues that a new
generation of experiments will have to address.